FRG: Collaborative Research: Mathematics of large scale urban crime

这个多学科的项目旨在开发新的数学方法，结合非线性偏微分方程组理论、统计力学、图论和统计学，用于城市犯罪的预测和控制。该项目侧重于时空犯罪模式，包括(1)针对犯罪热点的离散和连续模型对犯罪数据进行新的数学分析和比较；(2)具有空间嵌入的社会网络的模型，特别是关于帮派活动的模型；(3)探索新的地理概况方法，在现有模型中纳入城市地形的详细特征和更准确的犯罪活动模式。这个项目的数学工作包括非线性PDE模型的分析，统计物理模型的分析，以及这些模型的进一步发展，以包括空间异质性，不同的罪犯运动模式，以及城市街头帮派网络。同时，它为城市犯罪模式形成背后的机制提供了更深入的理解，并为当地执法机构提供了一些有用的算法和软件。犯罪数学是应用数学中的一个新兴课题，在全球范围内都有兴趣，与美国国土安全直接相关。这个重点研究小组涉及主要专长在非常不同的领域--数学、物理、人类学和犯罪学--的研究人员之间的互动，以便从非常不同的观点和角度来剖析和理解犯罪活动的模式形成。该项目涉及用于分析真实现场数据的算法开发和基于代理的城市犯罪模拟工具。这项研究还将开发新的城市犯罪模型，并对这些模型进行数学分析。该项目涉及对各级学生和博士后学者的培训，包括一个重要的本科生部分。博士生和博士后学者也将获得宝贵的指导经验，这是他们发展研究事业所必需的。这项工作包括与当地执法机构和纯粹数学和应用数学研究所的直接互动。

This multidisciplinary project aims to develop new mathematical methods, at the interface of the theory of nonlinear partial differential equations, statistical mechanics, graph theory, and statistics, for predictability and control of urban crime. The project focuses on spatio-temporal crime patterns and includes (1) new mathematical analysis and comparisons to crime data for discrete and continuum models of crime hotspots; (2) models with spatially embedded social networks, especially with regard to gang activity; and (3) exploration of new methods of Geographic Profiling, incorporating detailed features of urban terrain and more accurate modes of criminal movement into existing models. Mathematical work on this project includes analysis of nonlinear PDE models, analysis of statistical physics models, and further development of these models to include spatial heterogeneity, different offender movement patterns, and urban street gang networks. At the same time it provides both a deeper understanding of the mechanisms behind pattern formation in urban crime and some useful algorithms and software for local law enforcement agencies.Mathematics of criminality is an emerging topic in applied mathematics with interest on a global scale and direct relevance to U.S. homeland security. This focused research group involves interactions between researchers whose primary expertise lies within very different fields -- mathematics, physics, anthropology, and criminology -- so that pattern formation of criminal activity is dissected and understood from very different viewpoints and perspectives. The project addresses algorithm development for analyzing real field data and agent-based simulation tools for urban crime. The research will also develop new models for urban crime and carry out mathematical analysis of these models. The project involves training of students and postdoctoral scholars at all levels, including a significant undergraduate component. Ph.D. students and postdoctoral scholars will also obtain valuable mentoring experience necessary for development of their research careers. The work includes direct interaction with local law enforcement agencies and the Institute for Pure and Applied Mathematics.